Foster had gifted Stoke substitute Ryan Shotton a last-gasp winner in the last home game – but atoned with superb stops in quick succession on Saturday to keep out Cottagers defender John Arne Riise’s free-kick and substitute Bryan Ruiz’s follow-up.
The visitors, still without a league win this season, dominated the first period with skipper Danny Murphy dictating play but Albion posed more of a threat in the second period.
Peter Odemwingie looked lively for the Baggies when pushed upfront for the second 45 minutes but Fulham held firm with centre-back Brede Hangeland marshalling his defence well.
West Brom were the first to threaten with skipper Chris Brunt getting on the end of a Nicky Shorey cross but his powerful header was directed straight at Mark Schwarzer.
Then Youssouf Mulumbu dispossessed Pajtim Kasami 20 yards out and his low drive forced a sprawling save by Schwarzer to his right.
But it was two rare moments of danger for Fulham who dominated the remainder of the first half.
Murphy found Orlando Sa in space inside the box but a fine block tackle by Gareth McAuley deflected his shot for a corner.
Albion had a let-off after 12 minutes when Foster spilled a low shot from Clint Dempsey and the rebound was converted by Kasami – but replays showed he was offside.
The Albion fans were becoming frustrated at the amount of possession being enjoyed by the visitors who were not being closed down quickly enough.
Striker Shane Long was too isolated up front for West Brom in a 4-5-1 formation and lack of support meant him attempting a shot from a narrow angle which flew harmlessly over the bar.
Jol’s side were increasingly looking the more likely to break the deadlock with McAuley blocking a Sa attempt on the edge of the box and Foster clinging onto a Dempsey header.
Albion reverted to a 4-4-2 formation for the second period with Odemwingie pushing up front alongside Long.
But initially Fulham still looked the more dangerous and twice went close to going ahead.
The woodwork came to West Brom’s rescue when defender Jonas Olsson inadvertently deflected a volley by Dempsey against his own bar.
Then Dembele found himself unmarked 15 yards out but could not keep his shot down.
Hangeland became the first player to be booked after bringing down Long and then Grygera was yellow carded for fouling Thomas.
Albion appealed in vain for a penalty after a challenge on Long by Chris Baird.
Odemwingie had a great chance to put Albion in front after 64 minutes when he ran on to a through ball from Mulumbu but he shot straight at Schwarzer.
Baird became the third Fulham player to be booked for hauling down Odemwingie.
Only a superb double save by Foster prevented Ruiz from making an immediate impact.
The former Manchester United keeper blocked a fiercely driven free-kick by Riise with Foster then up quickly to turn the follow-up effort from Ruiz onto a post from two yards out.
Brunt nearly earned Albion victory in injury-time when his low cross-shot hit the post and Sa fired over at the other end.